Self-paced Gaussian-based graph convolutional network: predicting travel flow and unravelling spatial interactions through GPS trajectory data

Spatial interaction research is particularly important for geographical analyses, as it plays a crucial role in extracting travel patterns. However, previous studies on spatial interactions have not adequately considered regional population variations over time, resulting in insufficiently precise travel predictions. Moreover, the threshold of spatial correlations is difficult to determine. Existing studies have assumed fully connected spatial correlation matrices, which is not realistic. To address these limitations, we proposed the Self-paced Gaussian-Based Graph Convolutional Network (SG-GCN) to automatically estimate the threshold of spatial correlations for travel flow predictions. It incorporates a temporal dimension into spatial relationship matrices to enhance the accuracy of vehicle flow predictions. In particular, Gaussian-based GCN identifies patterns in a time series of regional flows, enabling more precise capturing of spatial relationships while fusing node and edge features. Building on this model, self-paced contrastive learning automatically sets thresholds to determine the presence or absence of spatial relationships. The model's performance was verified through two empirical case studies conducted in New York City, USA, and Ningbo, China, using 2.8 million bicycle-sharing records and 1.25 million taxi trip records, respectively. The proposed model helps delineate mobility patterns in cities of varying scales and with different modes of transportation.